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J. Phys. Chem. C 2009, 113, 15320–15325
Quantitative Voltammetry in Weakly Supported Media. Two Electron Transfer, Chronoamperometry of Electrodeposition and Stripping for Cadmium at Microhemispherical Mercury Electrodes Juan G. Limon-Petersen, Edmund J. F. Dickinson, Neil V. Rees, and Richard G. Compton* Department of Chemistry, Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford, OX1 3QZ United Kingdom ReceiVed: May 20, 2009; ReVised Manuscript ReceiVed: July 3, 2009
Double potential step chronoamperometry for the two-electron transfer amalgam-forming deposition and stripping of cadmium at a hemispherical mercury electrode in aqueous solution containing different concentrations of supporting electrolyte is compared with simulated results using the Nernst-Planck-Poisson system of equations. The latter were generated using an approximation of zero electric field at the interface [J. Phys. Chem. C 2008, 112, 13716-13728]; the approximation gives a good agreement between theory and experiment, so validating its use for the description of macroelectrode and microelectrode (but not nanoelectrode) problems involving low or negligible levels of supporting electrolyte. 1. Introduction Electrochemical experiments, particularly voltammetry, are usually conducted with the presence of high electrolyte concentrations, often achieved by the addition of “supporting electrolyte,” the role of which is simply to increase the ionic strength and conductivity of the solution. In turn, these charges cause the double layer at the electrode solution interface to become compressed to short ( τs and expanding proportionally to τ thereafter. Optimal parameters for the finite difference mesh density were established using detailed convergence studies at varying csup. All simulations were programmed in C++ and run on a desktop computer (Pentium 4 3.4 GHz processor, 2 GB of RAM), with running times of 10-20 min per simulation being typical. 3. Experimental Section
R)1
(26)
where the factor 4 arises from multiplication of the area of the hemisphere, A ) 2πre2, by the number of electrons transferred, n ) 2.
All solutions were made with ultra pure water with resistivity >18.2 MΩ cm at 25 °C and thoroughly degassed for 30 min with N2 (BOC, High Purity Oxygen free) before starting each experiment. All of the experiments were carried out under thermostatic control at 298 K using a water bath. Potassium nitrate (>98%, Aldrich), cadmium(II) nitrate tetrahydrate (>98%,
Quantitative Voltammetry in Weakly Supported Media TABLE 1: Values Used for the Numerical Simulations parameter Ef0 DCd2+ DCd/Hg DK + DNO-3 R re
value
source
-0.6 V vs SCE 0.60 × 10-5 cm2 s-1 1.4 × 10-5 cm2 s-1 1.8 × 10-5 cm2 s-1 1.9 × 10-5 cm2 s-1 0.5 5.0 × 10-4 cm
Macero14 Ikeuchi et al.12,13 Ikeuchi et al.12,13 Lobo et al.16 Hashitani17
Aldrich), mercury(I) nitrate (>98%, Aldrich), and nitric acid (70% W/W, Fischer Scientific) were used without any further purification. A three electrode cell was used. The working electrode was a mercury microhemisphere of radius 50 µm prepared according
J. Phys. Chem. C, Vol. 113, No. 34, 2009 15323 the procedure in Limon-Petersen et al.8,11 A saturated calomel electrode was used as the reference electrode and a platinum wire was used as a counter electrode. Solutions containing 3 mM of cadmium(II) nitrate and different concentrations of potassium nitrate as supporting electrolyte were used (300, 30, and 3 mM). The depositionstripping of cadmium was studied via double potential step chronoamperometry using a µAutolab type III (EcoChemie, Netherlands). In the first potential step cadmium is deposited at -0.70 and -0.80 V vs SCE in the hemisphere, and in the second potential step cadmium is stripped at -0.40 V vs SCE. The amount of cadmium deposited in the hemisphere is determined by the length of time of the deposition, so different deposition time lengths are analyzed.
Figure 3. Comparison between experiment (circles) and simulation (line) of 3 mM cadmium deposition (A-C) at two different potentials -0.7 and -0.8 vs SCE and stripping (D-F) at -0.4 vs SCE, at different supporting electrolyte 300 (A and D), 30 (B and E), and 3 (C and F). The current and time axis are noted in logarithmic scale.
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TABLE 2: Values used for the Numerical Simulations for Comparison between Single and Double Electron Transfer parameter
value
CA norm Csup φDep φStr DA DA/Hg DSup+ DSupR re
10 mM 0.5, 5, and 50 -0.25 V vs E0 0.25 V vs E0 1 × 10-5 cm2 s-1 1 × 10-5 cm2 s-1 1 × 10-5 cm2 s-1 1 × 10-5 cm2 s-1 0.5 5.0 × 10-4 cm
The experiment with the highest support was analyzed via the Cottrell equation to obtain the diffusion coefficient of Cd2+. We obtained a value of 6.0 × 10-6 cm2 s-1 which compares with the literature values by 6.7 and 7.0 × 10-6 cm2 s-1 by Ikeguchi et al.12,13 and Macero.14,15 4. Results and Discussion A double potential step was carried out at a 50 µm radius mercury microhemisphere electrode, in a solution containing 3 mM of cadmium nitrate and 300 mM of potassium nitrate. The first potential step was in order to deposit cadmium at the mercury hemisphere, forming an amalgam using a potential of -0.7 V vs SCE. The response is shown in the Figure 2A (solid line), which corresponds to a purely Cottrellian behavior with
Figure 5. Comparison between one electron (continuous line) and two j sup 50 (A), 5 (B), (dotted line) transfer at different concentrations of C and 0.5(C). The current and time axis are noted in logarithmic scale.
Figure 4. Simulated potential profiles for single one electron (continuous line) and two (dotted line) transfer (at t ) 0.02 s) at different j sup 50 (A) and 0.5 (B). concentrations of C
a t-0.5 dependence at short times. Next an oxidative potential at -0.4 V vs SCE was applied, stripping the cadmium from the hemisphere and obtaining the same t-0.5 dependence at short times. Then at longer times the t-0.5 dependence is lost due to the depletion of the cadmium in the mercury hemisphere. The same procedure was repeated in experiments where the concentration of supporting electrolyte was lowered to 30 and 3 mM respectively. The results of these experiments no longer show a Cottrellian time-dependence in the current response. Rather, they exhibit a flattened region at short times after the potential step (see Figure 2 dashed and dotted lines), and at
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longer times they show a higher current response where the electrolyte concentration is lowered (Figure 2A dotted and dashed). This behavior in the low support cases can be understood by noting that in fully supported voltammetric experiments the supporting electrolyte represents almost all of the charged species in the solution. So, when charge is transferred to or from the electrode, the charged species nearby (mostly supporting electrolyte) migrates in order to compensate for the distortion of the electric field. By contrast, in the case where supporting electrolyte concentration is very similar to the concentration of electroactive species, both of them migrate in approximately equivalent proportions to compensate the electric field distortion in the solution. Therefore, the electroactive species (in the case of the deposition) is attracted to the electrode, and hence at long times, the current is higher in the cases with lower support. Even though the migration in the solution mitigates the electric field within it, an ohmic drop is created through the solution, which is the rate limiting factor for the flat region in the transients at short times. These differences can be appreciated by examining panels A and B in Figure 2, where the magnitude of the flat regions can be seen to depend on the amount of supporting electrolyte added to the solution. The experimental results were compared with the simulations outlined above and using the parameters in Table 1; the value given to K0 was sufficiently large to induce reversible electrochemical behavior and hence not to influence the voltammetric response. Good agreement of experiment with the theoretical results in Figure 3 was found. This indicates to us that the theory is able to simulate a double electron transfer. In a previous paper, the use of this theory for single charge transfer has also been demonstrated.8 Together these observations provide validation of the zero field approximation advocated above and elsewhere2 for the modeling of weakly supported voltammetry at macroelectrodes and microelectrodes (but not nanoelectrodes). 4.1. Comparison between Single and Multiple Electron Transfer. In order to compare theoretically the physical outcome of single and multiple electron transfer, the parameters shown in Table 2 were used. The concentration of supporting electrolyte was normalized by the charge on the electroactive species, to render equivalent the electric fields in solution for the cases of single and double electron transfer respectively. The parameter Cnorm sup represents a constant ratio of added charge to electroactive species charge present in solution norm Csup )
Csup zC*A
(27)
where Csup is the concentration of supporting electrolyte, C*A is the concentration of electroactive species and z is the charge transferred. The resulting chronoamperograms were rescaled by the number of electrons transferred, to show equivalent charge transfer per charge in solution. As expected, the adequately supported cases behave identically subject to this normalization when high overpotentials are applied (Figure 5A), and show a t-0.5 dependence characteristic of the purely diffusional case. Examination of the potential profiles shows no difference, because the migration of the electroactive species at this concentration of supporting electrolyte is negligible and does not influence the electric field (Figure 4A). This validates norm . the normalization by the parameter C sup
In cases with lower supporting electrolyte concentration (Figure 5, panels B and C) some differences in the normalized current response are noted both in the ohmic drop controlled region and at longer times. In the ohmic drop controlled region, the two electron process has higher normalized currents than the single electron process, when the diffusion coefficients of the electroactive species are kept equal. This is due to the increased involvement of the electroactive species with the electric field, such that the more highly charged species is more strongly attracted near to the electrode and is better able to compensate ohmic drop. At higher times, toward steady-state, the current remains higher (Figure 5) due to increased migration of the more highly charged species. These variations between different ionic charges result from differences in charge mobility: a doubly charged species migrates more easily than a single charged species with the same diffusion coefficients. 5. Conclusions It has been demonstrated that the model2 developed by using the Nernst-Planck-Poisson set of equations can be applied not just to single electron transfer, but equally to simulate multiple electron transfers, enabling us to understand their differences and similarities. In particular while diffusion-controlled current scales with the number of electrons transferred, higher currents are observed at low support ratios for more highly charged electroactive species, due to better ohmic drop compensation and more rapid migration. Further the zero field approximation used in the theory2 is validated for macro- and microelectrode by comparison of the predictions of the simulation against experiment. Acknowledgment. We thank the following for support: St John’s College, Oxford (E.J.F.D), EPSRC (N.V.R.), and CONACYT, Mexico (J.G.L.-P.). References and Notes (1) Dickinson, E. J. F.; Limon-Petersen, J. G.; Rees, N. V.; Compton, R. G. J. Phys. Chem. C 2009, in press. (2) Streeter, I.; Compton, R. G. J. Phys. Chem. C 2008, 112, 13716– 13728. (3) Palys, M. J.; Stojek, Z.; Bos, M.; Van der Linden, W. E. J. Electroanal. Chem. 1995, 383, 105–17. (4) Oldham, K. B.; Zoski, C. G. In ComprehensiVe Chemical Kinetics; Bamford, C. H., Compton, R. G., Eds.; Elsevier: Amsterdam, 1986; Vol. 26, Chapter 2. (5) Beto, M. F.; Touin, L.; Amatore, C.; Montenegro, M. I. J. Electroanal. Chem. 1998, 443, 137–148. (6) Ciszkowska, M.; Stojek, Z. J. Electroanal. Chem. 1999, 466, 129– 143. (7) Norton, J. D.; Benson, W. W.; White, H. S.; Pendley, B. D.; Abruna, H. D. Anal. Chem. 1991, 63, 1909–1914. (8) Limon-Petersen, J. G.; Streeter, I.; Rees, N. V.; Compton, R. G. J. Phys. Chem. C 2008, 112, 17175–17182. (9) Limon-Petersen, J. G.; Streeter, I.; Rees, N. V.; Compton, R. G. J. Phys. Chem. C 2009, 113, 333–337. (10) Svir, I. B.; Klymenko, O. V.; Compton, R. G. Radiotekhnika 2001, 118, 92. (11) Limon-Petersen, J. G.; Rees, N. V.; Streeter, I.; Molina, A.; Compton, R. G. J. Electroanal. Chem. 2008, 623, 165–169. (12) Ikeuchi, H.; Sato, G. Anal. Sci. 1991, 7, 631–634. (13) Ikeuchi, H.; Uchida, H.; Sato, G. Anal. Sci. 1990, 6 (2), 239–243. (14) Macero, D. J.; Ruffs, C. L. J. Electroanal. Chem. 1964, 7 (4), 328– 331. (15) Macero, D. J.; Ruffs, C. L. J. Am. Chem. Soc. 1959, 81, 2942– 2944. (16) Lobo, V. M. M.; Ribeiro, A. C. F.; Verissimo, L. M. P. J. Mol. Liq. 1998, 78, 139–149. (17) Hashitani, T.; Tanaka, K. J. Chem. Soc. Faraday Trans. 1 1983, 79, 1765–1768.
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